U.S. patent number 4,058,713 [Application Number 05/724,872] was granted by the patent office on 1977-11-15 for equalization by adaptive processing operating in the frequency domain.
This patent grant is currently assigned to General Signal Corporation. Invention is credited to Michael J. DiToro.
United States Patent |
4,058,713 |
DiToro |
November 15, 1977 |
Equalization by adaptive processing operating in the frequency
domain
Abstract
Equalization apparatus for a communication system transmitting
through a time or frequency spread medium. The message to be
transmitted is partitioned and transmitted in burst or frame by
frame form. Each frame comprises the message (unknown at the
receiver) followed by a test signal known at the receiver. Time
gaps are provided between the message and test signals to avoid
overlapping of the received message and test signals due to
time-spreading. The received mutilated signals are processed in the
frequency domain to obtain a reconstituted version of the
transmitted message in the frequency domain. This is re-transformed
into the time domain so that the reconstituted message available at
the receiver is a close replica of the message which was originally
available only at the transmitter.
Inventors: |
DiToro; Michael J. (Massapequa,
NY) |
Assignee: |
General Signal Corporation
(Rochester, NY)
|
Family
ID: |
24912268 |
Appl.
No.: |
05/724,872 |
Filed: |
September 20, 1976 |
Current U.S.
Class: |
708/305; 333/18;
455/69; 708/404; 375/231; 455/67.14; 333/28R; 327/552 |
Current CPC
Class: |
H04B
7/005 (20130101) |
Current International
Class: |
H04B
7/005 (20060101); G06F 015/34 () |
Field of
Search: |
;235/152,156
;324/77R,77B ;325/41,42,65,473 ;328/167 ;333/18,28R,7T |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Smith; Jerry
Attorney, Agent or Firm: Kleinman; Milton E. Green; Stanley
B.
Claims
What is claimed is:
1. A signal processor for processing a message signal received over
a time-spread or frequency-spread medium to produce an estimate of
the transmitted message signal in which a known signal is
transmitted along with said message signal and received therewith,
comprising:
a. first means for converting all said received signals to the
frequency domain;
b. second means for providing a representation of said known
signal;
c. processing means responsive to said first and second means to
produce an estimate of the transmitted message signal in the
frequency domain; and,
d. third means for converting the frequency domain form of the
estimate of said transmitted message signal to the time domain.
2. The apparatus of claim 1 wherein said second means provides a
time domain representation of said known test signal and said
processing means includes means to produce a frequency domain form
of said known test signal.
3. The apparatus of claim 1 wherein said second means provides a
frequency domain representation of said known test signal.
4. The apparatus of claim 1 in which said first means responds to
said received message signal m'.sub.i (t) and known test signal
b'.sub.i (t) to produce corresponding frequency domain form
M'.sub.i (f) and B'.sub.i (f) and said processing means provides
B(f)M'.sub.i (f)/B'.sub.i (f) wherein B(f) is the frequency domain
form of said known test signal.
5. The apparatus of claim 4 which includes means for determining
channel noise powder and said processing means multiplies the
quantity B(f)M'.sub.i (f)/B'.sub.i (f) by a noise related
quantity.
6. The apparatus of claim 5 including means for providing kN.sub.o
wherein 1/4>K>2 and N.sub.o is said channel noise power.
7. The apparatus of claim 6 which includes means for separately
comparing received known and received message signal power in a
plurality of frequency bands with said quantity kN.sub.o and for
reducing, to zero, a received message signal in any frequency band
if, for that band, kN.sub.o is greater than either received known
or received message signal power.
8. The apparatus of claim 1 in which said first means produces a
transform B'.sub.i (f) for said received known signal b'(t) and a
transform M'.sub.i (f) for said received message signal m'.sub.i
(t), each transform comprising a series of Fourier coefficients
related to the contribution to the associated signal in a different
frequency band,
said processing means producing a further transform related to the
transmitted message signal and comprising a series of Fourier
coefficients, by computing
means for detecting channel noise power N.sub.o, and producing a
signal kN.sub.o,
means for comparing kN.sub.o with .vertline.B'.sub.i
.vertline..sup.2 and .vertline.M'.sub.i .vertline..sup.2 in each
said frequency band and for reducing the associated Fourier
coefficient of M" to zero if kN.sub.o >.vertline.B'.sub.i
.vertline..sup.2 or kN.sub.o >.vertline.M'.sub.i
.vertline..sup.2.
9. The apparatus of claim 8 wherein 1/4<k<2.
10. The apparatus of claim 8 in which said processing means further
includes fourth means for multiplying the product B(f)M'.sub.i
(f)/B'.sub.i (f) by G.sub.o wherein G.sub.o is a noise related
parameter.
11. The apparatus of claim 10 wherein said fourth means includes
means for computing ##EQU1##
12. A communications system for communicating message signals from
a transmitting station to a geographically remote receiving station
over a time-spread or frequency-spread medium including:
transmitting apparatus, at said transmitting station, responsive to
a message signal to transmit the same interleaved with a known
signal.
receiving apparatus at said geographically remote receiving station
responsive to the received form of said message signal and said
known signal, to provide an estimate of the transmitted form of
said message signal, said receiving apparatus including:
a. means for converting all said received signals to the frequency
domain;
b. second means for providing a representation of said known test
signal;
c. processing means responsive to said first and second means to
produce an estimate of the transmitted message signal in the
frequency domain; and,
d. third means for converting the frequency domain form of the
estimate of said transmitted message signal to the time domain.
13. The apparatus of claim 12 wherein said second means provides a
time domain representation of said known test signal and said
processing means includes means to produce a frequency domain form
of said known test signal.
14. The apparatus of claim 12 wherein said second means provides a
frequency domain representation of said known test signal to said
processing means.
15. The apparatus of claim 12 in which said first means responds to
said received message signal m'.sub.i (t) and known test signal
b'.sub.i (t) to produce corresponding frequency domain form
M'.sub.i (f) and B'.sub.i (f) and said processing means provides
B(f)M'.sub.i (f)/B'.sub.i (f) wherein B(f) is the frequency domain
form of said known test signal.
16. The apparatus of claim 15 which includes means for determining
channel noise power and said processing means multiplies the
quantity B(f)M'.sub.i (f)/B'.sub.i (f) by a noise related
quantity.
17. The apparatus of claim 16 including means for providing
kN.sub.o wherein 1/4<k<2 and N.sub.o is said channel noise
power.
18. The apparatus of claim 17 which includes means for separately
comparing received known and received message signal power in each
said frequency band with said quantity kN.sub.o and for reducing,
to zero, a received message signal in any frequency band if, for
that band, kN.sub.o is greater than either received known or
received message signal power.
19. The apparatus of claim 12 in which said first means produces a
transform B'.sub.i (f) of said received known signal b'.sub.i (t)
and a transform M'.sub.i (f) for said received message signal
m'.sub.i (t), each transform comprising a series of Fourier
coefficients related to the contribution to the associated signal
in a different frequency band,
said processing means producing a further transform related to the
transmitted message signal and comprising a series of Fourier
coefficients by computing M".sub.i (f) = M'.sub.i (f)B(f)/B'.sub.i
(f),
means for detecting channel noise power N.sub.o, and producing a
signal kN.sub.o.
means for comparing kN.sub.o with .vertline.B'.sub.i
.vertline..sup.2 and .vertline.M'.sub.i .vertline..sup.2 in each
said frequency band and for reducing the associated Fourier
coefficient of M".sub.i to zero if kN.sub.o is greater than
.vertline.B'.sub.i .vertline..sup.2 or .vertline.M'.sub.i
.vertline..sup.2.
20. The apparatus of claim 19 in which 1/4<k<2.
21. The apparatus of claim 19 in which said processing means
further includes fourth means for multiplying the product
B(f)M'.sub.i (f)/B'.sub.i (f) by G.sub.o wherein G.sub.o is a noise
related parameter.
22. The apparatus of claim 21 wherein said fourth means includes
means for computing ##EQU2##
23. The apparatus of claim 12 in which said transmitting means
transmits a known signal having a substantially flat frequency
spectrum throughout a frequency band of interest.
24. The apparatus of claim 12 in which said transmitter transmits
in burst form and interleaves a known signal burst within each pair
of message bursts.
25. The apparatus of claim 24 in which said known signal has a
substantially flat frequency spectrum.
26. The apparatus of claim 25 in which said known signal comprises
a pulse sequence 1111100110101.
Description
FIELD OF THE INVENTION
The present invention relates to communication systems, and more
particularly, to improvements in such communication systems in
which equalization is provided for the transmission function, by
apparatus processing received signals in the frequency domain.
BACKGROUND OF THE INVENTION
Various forms of communication links exhibit time-frequency spread
which can make it difficult to recover a transmitted message so as
to make available at the receiver a faithful reproduction of the
message which has been transmitted. Examples of such media are HF
links via the earth-ionispheric duct, underwater sonic and earth
seismic links, troposcatter VHF links, and to some lesser extent,
voice-quality telephone lines. Transmission difficulties are caused
by a number of effects, such as multi-path reception, group delay
distortion or, in general, time-spread of the time response of the
overall transmission system. In addition, there also occurs
Doppler, time-jitter, time-variable frequency offset or, in
general, frequency spread of the overall response of the
transmission system.
In order to overcome the undesirable waveform linear distortions
that these effects introduce into the received form of a
communicated message, the prior art has primarily processed the
received signal in the time domain (see e.g., "Communication in
Time Frequency-Spread Media Using Adaptive Equalization" by M. J.
DiToro, found in the Proceedings of the IEEE, Volume 56, Number 10,
October 1968, pages 1653-79). The ultimate goal of the prior art
techniques, which is in common with the goal of this invention, is
to provide at the receiver a reconstituted message which faithfully
reproduces the message which was made available to the transmitter
for transmission purposes. The present invention seeks, however, in
distinction to the prior art, to achieve this result by processing
the received message in the frequency domain rather than by
operating on the received message in the time domain.
Therefore, it is one object of the present invention to provide a
communication system in which the received message is processed, in
the frequency domain, so as to provide a faithful reproduction of
the message which was made available to the transmitter. It is
another object of the invention to provide apparatus for use at a
receiving station, for processing the received message in the
frequency domain, so as to make available faithful reproductions of
the message that was actually transmitted. It is still another
object of the present invention to provide apparatus as is set
forth above, which takes into account, in the processing, noise
which may be received along with the message so that the ultimate
reconstructed message made available is only to a small degree
contaminated by noise.
If the transmission medium transfer function were known, the
transmitted message could be reconstituted at the receiver by a
de-convolution process since the received message is the
convolution of the transmitted message and the transmission medium
impulse response function. De-convolution in the time domain is
difficult to achieve. However, in the frequency domain
de-convolution is more tractable and is done simply by division
wherein the transmitted message can be obtained by dividing the
Fourier transform coefficients of the received message by the
Fourier coefficients of the medium transfer function. This is a
much more tractable problem.
SUMMARY OF THE INVENTION
The present invention achieves the objects herein above set forth,
as well as other objects of the invention, by transmitting a
message signal in burst form interleaved with a known test signal,
receiving the transmitted signals and converting them, along with
the transmitted form of the known signal, to the frequency domain,
processing all the signals converted to the frequency domain in
order to produce a reconstituted version of the transmitted message
signal, in the frequency domain and reconverting the reconstituted
version of the transmitted message to the time domain.
To provide the receiver with a known test signal interleaved with
the message signal, the transmitter is arranged to segregate, in
the form of bursts, predetermined portions of the transmitted
message. Each burst is transmitted separately at a slightly higher
speed than the initial message speed so as to make available a time
gap during which a burst comprising the known test signals is
transmitted. The transmission of both the known test signals and
the message signal is timed so that, at the receiver, overlap of
the message and known signal, caused by time-spread, is
avioided.
At the receiver, the received message and known test signal are
converted into the frequency domain. Comparing the transmitted and
received forms of the known signal enables the apparatus to obtain
an estimate of the transfer function of the transmission media
which can then be employed to develop the transmitted message
signal. In the absence of noise the apparatus could then convert
the processed signal into the time domain and then, employing known
apparatus, coalesce the different disjointed bursts of the
transmitted form of the message signal into a continuous signal.
However, in order to cope with unavoidable noise added to the
received message and known test signal, apparatus is provided to
determine a measure of the noise contribution at the different
frequencies. With this information, a dynamic weighting function is
provided, as a function of frequency, which may be employed to
modify the result of the previous processing. As modified, then,
the apparatus converts the frequency domain version of the
transmitted message signal into the time domain. At this point, the
apparatus has available a plurality of time-spaced bursts of the
estimate of the transmitted signal. From these time-spaced bursts,
a continuous message is reconstituted which then faithfully
corresponds to the form in which the message was made available for
transmission purposes .
BRIEF DESCRIPTION OF THE DRAWINGS
The remaining portion of this specification will describe a
preferred embodiment of the invention when read in conjunction with
the attached drawings, in which like reference characters identify
identical apparatus, and in which:
FIG. 1A is a diagramatic showing of one application of the
invention;
FIG. 1B is a representative waveform illustrating the message to
transmitted;
FIG. 1C is a segmented speeded-up message interleaved with the test
signal in accordance with the preferred embodiment of the
invention;
FIG. 1D is the result when the waveforms of FIG. 1C are transmitted
through the medium;
FIG. 2 is a block diagram of a transmitter which can be employed in
a communication system employing the principles of the
invention;
FIG. 3 is an exemplary timing diagram of some signals employed in
the apparatus illustrated in FIG. 2;
FIG. 4 is a block diagram of the apparatus at the receiver designed
to apply the principles of the invention;
FIG. 5 is an exemplary timing diagram showing several of the
signals developed in the apparatus of FIG. 4;
FIGS. 6A and 6B comprise a functional block diagram illustrating
the processing carried out by the FFT processor, shown in block
form in FIG. 4; and
FIGS. 7A-7P are waveforms defining and illustrating the result from
a simulation of the invention.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
In the general case of transmitting through a medium exhibiting
both time-spread (or smearing) and frequency-spread (or
time--variability) a transmitted signal undergoes a variety of
impairments which can be characterized as:
1. dispersion, multi-path reception, group delay distortion, or, in
general, time-spread of the response of the overall transmission
system to a delta function in time; and,
2. doppler, time-jitter, time-variable frequency offset, or, in
general, frequency spread of the response of the overall
transmission system to a delta function in frequency, i.e., a CW
signal.
Regardless of the specific type of modulation employed, the goal of
the receiver is to process the received signal so that the
information contained in the transmitted signal can be derived from
the output of the receiver, i.e., the processed received signal.
Examples of transmission media which exhibit the impairments
referred to above are HF links via the earth-ionispheric duct,
underwater sonic and earth seismic links, troposcatter VHF links,
and, with less time variability, voice-quality telephone lines.
FIG. 1A is a schematic representation of a multi-path HF
ionispheric transmission system in which a transmitting station T
transmits signals to a receiving station R, which is below the line
of sight (LOS) from the transmitting station, via the ionispheric
duct.
In the general case, the message m(t) at terminal T is continuous
as in FIG. 1B. This is segmented into a plurality of message bursts
such as m.sub.1 (t), m.sub.2 (t), etc., as shown in FIG. 1C.
Because the message burst is transmitted at a rate faster than the
initial message m(t) gaps are created between contiguous message
bursts. Into these gaps a known test signal b(t) is transmitted,
that is, a signal which is known at the receiver. Although the
known signal could be time-dependent, in the simplest case it is
time invariant, and will be represented hereinafter as b(t). In
order to enable the receiver to readily distinguish a received
version of the known test signal and the message signal, gaps (as
in FIG. 1C) in the transmitted signal are provided between the
message signal bursts and the known signal bursts so that
notwithstanding the time-spread encountered in the transmission
process, the bursts do not overlap in time at the receiver.
At the receiver, this transmission sequence takes the form
illustrated in FIG. 1D, wherein b.sub.1 '(t), b.sub.2 '(t), etc.,
represent different received smeared known signal bursts, m.sub.1
'(t), m.sub.2 '(t), etc., represent different received smeared
message bursts. FIG. 1D illustrates that the signal sequences do
not, in fact, overlap in time at the receiver.
If we assume that the transmission medium is time-invariant over a
short period of time, or that it is slowly varying, then, in the
frequency domain, we can write the following expressions:
and
Capitalization, e.g., H.sub.i (f), indicates the Fourier
coefficient of the corresponding lower case time waveform, e.g.,
h.sub.i (t). B(f) refers to the (invariant) transmitted known
signal while B'.sub.i (f) refers to the received known signal,
M.sub.i (f) refers to the transmitted message signal burst and
M'.sub.i (f) refers to the received form of the message signal.
In these expressions, the integer i is the frame number, e.g., 1,
2, etc.
Substituting, in the second equation, the known terms of the first
equation, we can thus write an expression in the frequency domain
for the transmitted message signal as follows:
where the reconstructed M".sub.i (f) is close to M.sub.i (f).
Based on the foregoing, then, the apparatus of the invention
converts the time domain form of the received signals to frequency
domain form and then obtains an estimate of the transmitted message
in the frequency domain.
We have indicated that the foregoing is based on the assumption
that the transmission media is slowly varying. This assumption
depends, of course, to some extent, on the portion of the
transmission spectrum which we are employing, as well as another
factor which must be considered because the transfer function of
the transmission media is being evaluated by the known signal at
one time and the message signal is, of course, transmitted at some
time later. I have found, however, that for HF transmission,
adequate results are obtained if we send 10 to 20 frames per second
where a frame is comprised of a known signal burst and a message
signal burst. For purposes of maximizing through put, of course, it
would be desirable to reduce the duration of the known signal burst
to some minimum duration. On the other hand, in order to obtain an
accurate estimate of the transmission media characteristic, the
known signal should be sufficiently long to obtain a fairly precise
estimate of the transmission media throughout the spectrum of
interest.
The foregoing representation of the problem also ignores the effect
of noise. More particularly, both the received message signal and
the received known test signal include noise therein. In order to
accurately process the received form of the message signal in order
to generate or recreate the transmitted form of the message signal,
some means must be provided to eliminate, from the received form of
the message signal, that portion which arises from a noise source.
Therefore, instead of the expression reproduced above, the
apparatus of my invention employs the following expression:
In the foregoing expression, the parameters have their previously
defined meaning, and the parameter G.sub.o (f) is a scalar
multiplier to eliminate the effects of noise. Those skilled in the
art will realize the quantities M'.sub.i (f), B(f), B'.sub.i (f),
M".sub.i (f) are complex Fourier coefficient quantities having
different values at each of a plurality of frequencies and that
G.sub.o (f) is a different scalar quantity at each of a plurality
of frequencies.
A preferred embodiment of the invention will now be disclosed with
reference to FIGS. 2-6B.
FIG. 2 is a block diagram of the apparatus at the transmitting
station T, arranged to generate the signal sequence of FIG. 1C
going to the RF transmitter. As is shown in FIG. 2, a message
source 11 supplies signals to a multiplier 14, and a phase locked
loop 12. The phase locked loop 12 provides timing information to a
synchronizing generator 13, the outputs of which are supplied to
access or address ROM's 15 and 19 as well as the RAM's identified
as burst memories 17 and 18. The particular timing of these various
sync outputs of sync generator 13 will be illustrated with
reference to FIG. 3. The output of multiplier 14 is provided as an
input to both burst memories 17 and 18. A carrier generator 16,
synchronized to PLL 12, feeds a modulator 20, whose output is made
available to an RF transmitter 21 for radiation via antenna 22. The
other input to modulator 20 is derived from either burst memory 17
or 18 or ROM 19. Each of the foregoing structures are well known to
those skilled in the art and a detailed disclosure thereof is not
deemed necessary.
Message source 11 represents the source of message information
which can comprise any message source (such as a telephone system)
analog or digital, which supplies information in the form of a
varying electrical signal. In the case of an analog message source,
digitizing apparatus would be required so that the message is
provided to the transmitting apparatus in pulse form. Preferably,
these can be binary pulses employing binary signals in which a word
of information is made up of a number of signals having one of two
possible amplitudes. Phase locked loop 12 allows the
synchronization generator 13 to be synchronized with the rate at
which information is received from the message source 11, the
reason for which will become clear hereinafter. As is shown in FIG.
1C, the incoming message will be transmitted in burst form, with
the known signal transmitted in the gaps between different bursts
of the message signal. In order to provide the gap, the message
signal must be transmitted at a rate faster than it is received,
and to form the message into separate bursts, random access
memories 17 and 18 are provided. In order to provide for message
randomization, however, the multiplier 14 multiplies the message,
as it is received, by a pseudo-random sequence contained in ROM 15.
As a message is received, and randomized, it is inserted into one
or the other of burst memories 17 and 18. In the period of time
when one memory is being written into, the other burst memory is
read out and then the roles of the burst memories are interchanged.
For example, if a message is being written into a burst memory 17,
burst memory 18 will be read out at a higher rate than the rate at
which the message is being received. When burst memory 17 is full,
burst memory 18 will be empty, and the message is then written into
burst memory 18, and burst memory 17 is read out. These operations
occur under the control of the synchronizing generator 13 which
produces the necessary synchronizing signals. For example, sync 2
and sync 4 enable writing into one or the other of the memories
whereas syncs 5 and 6 enable reading from one or the other of the
memories. After a message signal has been read out of a burst
memory, either 17 or 18, the known signal must be transmitted. The
known signal is contained in ROM 19, and readout of this memory is
initiated by sync 3.
FIG. 3 shows typical synchronizing sequence. For example, the first
line of FIG. 3 indicates an uninterrupted digital message beginning
at time to.
Contemporaneously with the beginning of the uninterrupted message,
sync 1 initiates readout of ROM 15, the randomization code. FIG. 3
indicates the length of this sequence. Contemporaneous with the
readout of ROM 15, synchronizing signal 2 enables the now
randomized message output of multiplier 14 to be written into burst
memory 17.
At the conclusion of the period during which memory 17 has a
message signal written therein, sync 1 is again produced to again
read out the sequence of ROM 15, only now, however, under the
control of sync 4 the randomized output of multiplier 14 is written
into memory 18. Substantially contemporaneous with sync 4, sync 3
is produced which enables readout of ROM 19. Stored in ROM 19 is a
known sequence, which is hereinafter referred to as the known test
signal or simply the known signal. Sync 3 enables the known signal
to be read out of ROM 19 and made available to modulator 20 for
transmission purposes. Thus, at the lowest line of FIG. 3, we see
that the known signal b(t) is provided to modulator 20. Shortly
subsequent to the production of sync 3, at the conclusion of the
known signal, sync 5 is produced which allows the message signal
now stored in memory 17 to be read out.
It is significant that the writing and reading time is
significantly different, implying that the message signal is read
out at a rate faster than it is written. Thus, the output of memory
17 provides the message signal to the modulator 20. Subsequent to
readout of memory 17, sync 2 is again produced so that the
randomized message can now be written into the now empty memory 17.
The sequence continues in this fashion so that alternate message
bursts are provided by either memory 17 or 18, and these message
bursts have located between them the outputs of ROM 19, the known
signal.
In order to provide the receiver with signals which do not overlap
in time, a hiatus is provided between termination of any known
sequence and the beginning of the next message signal, as well as
between the termination of any message signal and beginning of a
known signal. The hiatus should be at least as long as the time
spread to be encountered in the transmission medium. For example,
for a transmitting and receiving pair which are separated by 3,000
kilometers, 5 msec., would be a suitable hiatus. As will be
explained hereinafter it may be preferable to lengthen the hiatus
for an additional millisecond to enable the receiver to measure the
channel noise power in the absence of any signal. The reasons for
this will become clear hereinafter.
In the foregoing fashion, the apparatus shown in block form in FIG.
2 produces a transmitted signal sequence as shown in FIG. 1C.
The block diagram of the receiver is shown in FIG. 4. As shown in
this Figure, a radio frequency section 33 has the transmitted
signal coupled thereto by means of an antenna 32. The signal is
demodulated in demodulator 34 from which it drives a phase locked
loop 35, the output of which drives a sync generator 36. Sync
generator 36, as sync generator 13, develops synchronizing signals
for routing the received signals to the appropriate location. More
particularly, the output of demodulator 34 consists of the
demodulated version of the message signal m'.sub.i (t), the
demodulated version of a known signal b' (t), with a small hiatus
therebetween, followed by similar sequences. A pair of burst
memories 37 and 38 have written therein, respectively, signals
representing the received form of the known test and message
signal, under control of outputs of the sync generator 36. At the
appropriate time, the contents of the memories 37 and 38 are read
out and made available to the FFT processor 42. In addition, the
contents of ROM 39 can also be made available to the FFT processor
42, under the control of sync 11. Finally, the channel noise power,
measured by conventional apparatus 41, is also made available to
the FFT processor 42. The output of FFT processor 42 is coupled to
a memory 43, which can actually comprise a shift register. The
output of memory 43 is coupled to a multiplier 44, to which is also
coupled the output of ROM 40, which has stored therein the same
randomizing sequence as was stored in ROM 15 (see FIG. 2). The
output of multiplier 44 is made available to one of two random
access memories 45 and 46 under control of appropriate
synchronizing signals. Each of the memories stored a derandomized
reconstituted version of the transmitted form of the message burst.
The memories are alternately written into and read out of, so that
the signal sequence available at the output of memories 45 and 46
is the restored message, i.e., a de-bursting or continuous output
is provided.
FIG. 5 illustrates some of the timing signals and other outputs at
various portions of the receiving apparatus. More particularly, the
uppermost line in FIG. 5 illustrates the output of demodulator 34
showing both the received known signal and message signals, in
burst form. Sync 7 allows the received known signal to be written
into memory 37, whereas sync 8 allows the received message signal
to be written into memory 38. Contemporaneous with the writing
process of memory 38, the contents of memory 37 are made available,
as a consequence of sync 9, to the FFT processor 42. Sync 11, which
is produced at a time subsequent to sync 9, makes available to the
FFT processor 42 the contents of ROM 39, which contains the
transmitted form of the known signal. Subsequently, sync 10 allows
the contents of memory 38, containing the received form of the
message signal to also be made available to FFT processor 42. As is
shown in FIG. 5, the sequence continues, that is, after readout of
memory 37, sync 7 allows the subsequent received form of the known
signal to be written therein and the sequence continues. At some
point subsequent to the production of sync 10, the FFT processor 42
makes available to memory 43 the randomized estimate of the
transmitted form of the message signal. This is derandomized via
multiplier 44, under control of sync 12. A typical derandomized
sequence is then written into memory 45, for instance. The next
subsequent output of the FFT processor, after derandomization, is
written into burst memory 46. The sync signals then allow the
outputs of memories 45 and 46 to be read out, at a slower rate than
they are written into, so as to provide a continuous form of
signal.
The processing carried out by FFT processor 42, employing the
received forms of the known signal and message signal, along with
the transmitted form of the known signal will now be described with
reference to FIG. 6A and 6B.
FFT processor 42 may be implemented by means of a general purpose
digital computer operating under a program which will be apparent
from a review of FIGS. 6A and 6B, along with the associated
portions of the specification. Alternatively, special purpose
apparatus can be provided which is designed to carry out the
functions of FIGS. 6A and 6B. Those skilled in the art will readily
understand how such apparatus is to be constructed. A number of
elements in the processing are employed a plurality of times, and
for this reason it is preferable (although not necessary) to
"time-share" this apparatus. For example, reference to FIGS. 6A and
6B indicates that Fast Fourier Transform function is required in
four instances, multiplication is required in four instances, and
division is required in four instances. Thus, instead of providing
a different apparatus to perform each of these functions, for
example, one Fast Fourier Transfer circuit could be enabled to
perform each of the Fast Fourier Transform operations by
time-sharing that apparatus.
As shown in FIG. 6A (wherein the circled reference numerals
indicate that the associated signals come from the apparatus
identified by that reference numeral), the transmitted form of the
known signal is converted to the frequency domain by FFT unit 50A,
and stored in a memory 51. The FFT 50A thus responds to b(t) and
produces B .sub.i (f) which is stored in memory 51. In a similar
fashion, the received form of the known signal is converted to the
frequency domain and stored in a random access memory 53. That is,
b'.sub.i (t) is converted to B'.sub.i (f) and stored in memory 53.
Employing the convention that capitalized letters represent
frequency domain function (Fourier coefficients) and the primed
parameters refer to the received form of the signal, the memories
51, 52 and 53 store respectively B(f), B'.sub.i (f) and M'.sub.i
(f). The length of each of these sequences depends in part on the
precision to which the apparatus must be held and also determines,
of course, the size of the associated memories. Typically, for a
message burst of 64 bits, 128 complex Fourier coefficients would be
sufficient. Those skilled in the art will realize that the
foregoing is exemplary and can be varied to suit different
requirements of accuracy.
In any event, multiplying apparatus 54 provides the product
B(f)M'.sub.i (f) and divider 55 produces the result B(f)M.sub.i
'(f)/B'.sub.i (f). In line with the theoretical discussion above,
in the absence of noise, this is the frequency domain form of the
apparatus' estimate of transmitted message. In order to correct for
the presence of noise, however, the quantity G.sub.o (f) is
provided by the dynamic weighting apparatus 56. This factor is
multiplied by the previously computed quantity in multiplier 57.
The result is a quantity M".sub.i (f) corresponding to the Fourier
coefficients of the apparatus' estimate of the transmitted message
signal. Preparatory to obtaining the time domain form thereof, the
conjugate is obtained in apparatus 58 and the results stored in
memory 59. Fast Fourier Transform apparatus 50D obtains the inverse
Fourier Transform thereof, m".sub.i (t), and stores the result in
memory 43 (corresponding to that memory in FIG. 4).
FIG. 6B illustrates, in detail, the functions performed by the
dynamic weighting apparatus 56. More particularly, signal sequences
are made available to the apparatus of FIG. 6B, corresponding to
the quantities B'(f), M'(f) and the receiver noise power N.sub.o.
The dynamic weighting function G.sub.o (f) is generated to correct
the estimate of the message signal provided by divider 55 for the
presence of noise. The apparatus compares the power spectra of the
received form of the known and message signals with the noise
power, at each of a plurality of different frequencies
(corresponding to different Fourier coefficients). If noise power
in a certain frequency band exceeds the power of the associated
Fourier coefficient of either the received form of the known test
signal or the message signal, the corresponding Fourier coefficient
in the estimate of the message signal is set to zero. That is, the
quantity KN.sub.o is compared with .vertline.B'.sub.ij
.vertline..sup.2 and .vertline.M'.sub.ij .vertline..sup.2, wherein
i designates the frame and j designates the frequency band with
which the Fourier coefficient is associated. If kN.sub.o is greater
than .vertline.B'.sub.ij .vertline..sup.2 or .vertline.M'.sub.ij
.vertline..sup.2 then the associated estimate M".sub.ij is set to
zero. Although I have referred to apparatus in which k = 1, this is
not necessarily an optimum. I have employed k = 1/2 in tests. The
exact quantity k is best determined empirically. If the power of
both the received form of the known signal and the message signal
exceed the noise power, then a ratio is taken to derive the
quantity G.sub.o, and this ratio is employed to reduce the Fourier
coefficient of the estimate of the message signal provided by the
divider 55.
As shown in FIG. 6B, the Fourier Transform of both the received
form of the known and message signals are provided respectively to
conjugate apparatus 60 and 61. Each Fourier coefficient can be
though of as a complex number or vector. A conjugate apparatus
(such as 60 or 61) reverses the polarity of the imaginary portion
of the vector and provides the result to a multiplying apparatus 62
and 63. The multiplying apparatus multiplies the complex number and
its conjugate to obtain a quantity related to the power of the
signal at the associated frequency. Dividers 64 and 65 then divide
the noise power by either the received form of the known signal
power or the received form of the message power. The resulting
ratios N.sub.o /.vertline.B'.sub.ij .vertline..sup.2 and N.sub.o
/.vertline.M'.sub.ij .vertline..sup.2 are coupled to subtractors 67
and 68. These subtractors are also provided with a signal
corresponding to unity by ROM unit 66. If the result produced by
subtractor 67 or 68 is less than zero, then function 69 or 70 sets
the associated frequency parameter for the estimate of the
transmitted message signal (M".sub.ij) to zero. In other words, if
the noise power exceeds either the power of the received form of
the known signal or the message signal, then the apparatus
recognizes it cannot provide an accurate estimate of what the
original message was, at that frequency component, and therefore
sets it to zero. In line with the preceding discussion, it may be
preferable to generate the ratios kN.sub.o /.vertline.B'.sub.ij
.vertline..sup.2 and kN.sub.o /.vertline.M'.sub.ij .vertline..sup.2
or some monotonic function thereof and compare the ratios with
unity to determine if kN.sub.o is greater than .vertline.B'.sub.ij
.vertline..sup.2 or .vertline.M'.sub.ij .vertline..sup.2 , where k
is empirically determined. Assuming, however, that the difference
is greater than 0, then units 71 and 72 provide the square root of
the results to the adders 73 and 74, respectively. Also provided to
each of adders 73 and 74 is a signal corresponding to unity. The
result, respectively, 1 + .sqroot.1 - N.sub.o /.vertline.B'.sub.ij
.vertline..sup.2, and 1 + .sqroot.1 - N.sub.o /.vertline.M'.sub.ij
.vertline..sup.2 are provided to divider 76 which forms a ratio
corresponding to G.sub.o. For each frequency component or Fourier
coefficient, the dynamic weighting factor is computed and is
multiplied with the associated frequency component of the Fourier
coefficient provided by the divider 55 in the multiplier 57. The
output of multiplier 57 is a signal train comprising a series of
complex numbers comprising the Fourier coefficient of the estimate
of the transmitted message, corrected by the dynamic weighting
factor G.sub.o, in order to take into account the inaccuracies
produced by noise. The conjugate apparatus 58, like that apparatus
60 and 61, provides the conjugate of the complex number which is
then stored in a random access memory 59. The Fast Fourier
Transform unit 50D takes the inverse Fourier Transform and stores
it in a random access memory 43. The signal stored in memory 43
m".sub.i (t) is a time domain signal comprising the apparatus'
estimate of the originally transmitted message signal,
corresponding to the burst message which has now been
processed.
As is mentioned above, the remaining apparatus comprising
multiplier 44 and memories 45 and 46 serve to derandomize the
message estimate and to de-burst the form of it so as to produce,
at the output, the restored message in the form in which it was
originally transmitted.
FIGS. 7A-7P illustrate the product of a simulation of the foregoing
apparatus to demonstrate the effectiveness of the processing. FIG.
7A is the simulated time domain impulse response of the
transmission medium clearly illustrating multi-path reception. The
Fourier coefficient magnitudes of this is illustrated in FIG. 7B
and illustrates that certain portions of the spectrum have faded as
a result of multi-path transmission. Of course, the transmitting
and receiving apparatus has no way, a priori, of determining these
parameters. For simplicity of illustration, only the magnitudes of
the Fourier coefficients are shown in the spectra; it should be
kept in mind, nevertheless, that these Fourier coefficients are
complex quantities.
FIGS. 7C and 7D illustrate, respectively, the time sequence of the
known test signal and the Fourier coefficient magnitudes thereof.
The known signal is taken, for example, as the 13 bit Barker Code
1111100110101. Particularly noteworthy is the fairly constant
amplitude spread of the spectrum of this known test signal. FIG. 7E
illustrates the transmitted message signal (although not used in
the processing above, it is instructive to see FIG. 7F which is the
Fourier coefficient thereof).
FIGS. 7G and 7H are, respectively, the received smeared known test
signal and the Fourier coefficients thereof. Comparing FIGS. 7G and
7C, the considerable distortion and smearing introduced as a result
of transmission is readily apparent. For this simulation, the
channel signal to noise ratio for both the known signal and the
message signal were taken as 15DB. The received form of the message
signal is shown in FIG. 7I, and its Fourier coefficient is shown in
FIG. 7J. Comparing FIGS. 7E and 7I, readily points out the
substantial distortion in the message introduced through
transmission.
FIG. 7K illustrates the needed mutiplicative processing done on
FIG. 7J in accordance with this invention to obtain FIG. 7N which
is the Fourier coefficient of the receiver's estimate of the
originally transmitted message M".sub.i (f). Taking the inverse
Fourier Transform produces the time domain signal shown in FIG. 7O.
After peak-peak clipping and expanding the message for comparison
purposes, the result is the sequence illustrated in FIG. 7P.
Comparing the sequence illustrated in FIG. 7P with the originally
transmitted message, the sequence of which is illustrated in FIG.
7M, indicates that no errors have been made in transmission. For
comparison, FIG. 7L illustrates the output of the receiver where no
signal processing is carried out in accordance with this invention.
The small dashes in the lower portion of FIG. 7L illustrate bit
errors that have been made by the receiver, an error being whenever
the signals in FIG. 7M and 7L are different. The five bit errors in
the approximately 50 transmitted bit message represents a system
bit error of 0.1 which, for practical purposes, is useless as a
communication system.
In the foregoing description the processor has relied on a
comparison between the received form of the known signal and the
transmitted form of the known signal to arrive at an estimate of
the effect of the transmission medium on the transmitted signal so
as to restore the received form of the transmitted signal to its
original transmitted form. Since the apparatus employs only a
single transmission channel, and since only one of the known or
message signals can be transmitted at any one time, there is some
inherent time delay between the transmission of the known and
message signals which may result in some error due to changes in
the transmission media. One way to minimize this error is to
transmit the known signal sufficiently often to minimize changes in
the transmission media between different known signal bursts.
Increasing the rate of transmission of the known signal, of course,
reduces the throughput, and therefore the efficiency of the
communications system, since the goal of the communication system
is the transmission of message signals and not known signals. One
variant of the invention which can be employed to reduce the effect
of the delay between transmission of the known and message signals,
while at the same time maintaining reasonable throughput, is to
estimate the characteristics of the transmission medium based upon
comparisons between received and transmitted known tests signal
both preceding and subsequent to transmission of the message
signal. Where the estimates of the transmission media vary due to
changes in the relationship between the received and transmitted
forms of the known signal, the estimates will be weighted in favor
of the relationship closer in time. For example, at the beginning
portion of a message signal, the relationship between the received
and transmitted forms of the known signal preceding the message
signal would be weighted more than the relationship between the
received and transmitted form of the known signal subsequent to the
message. Likewise, for the portions of the message past its
midpoint, the relationship between the received and transmitted
forms of the known signals subsequent to the message would be
weighted in favor of the relationship between the received and
transmitted forms of the known signals prior to the message.
Modification of the apparatus disclosed herein to employ this
variant will be apparent to those skilled in the art. More
particularly, it will only be necessary to retain the estimate of
the transmitted message until after the succeeding known signal is
received and the relationship between it and its transmitted form
is determined before finalizing the estimate of the transmitted
message.
Mention has been made of the criteria for selecting the hiatus
between the termination of the transmitted known and message signal
and the beginning of the next transmitted signal, either message or
known, for the purpose of preventing overlap in these signals as
received. In order to measure the noise power, however, it is
preferable to have a hiatus in the signal at the receiver. To this
end, therefore, a further small hiatus can be developed at the
transmitter for this purpose. If desired, of course, the
measurement of the noise power could be synchronized, at the
receiver, to enable the measurement at the time when the hiatus is
expected.
The FFT process can be carried out with commercially available
equipment. The output of such unit is a pulse train corresponding
to different Fourier coefficients of different frequency terms of
the transform. The equations and functions disclosed above are
applicable, of course, only to corresponding terms of different
transforms. Multiplying B.sub.i M'.sub.i, for instance, requires
multiplying corresponding coefficients only. That is, the
expression is the sum of B.sub.ij M'.sub.ij for all j. Effecting
this is well within ordinary skill of the programmer or signal
processing circuit designer. Accordingly, the details of such
apparatus need not be disclosed. Apparatus to produce the conjugate
of a vector quantity, and for multiplying, dividing, adding and
subtracting are functions also well within the skill of the
routineer.
FIG. 4 also illustrates ROM 39 which stores, as described in the
specification, the transmitted form of the known test signal, b(t).
The specification describes that FFT 42 derives B(f) from this
sequence for processing each message burst. Inasmuch as this is an
invariant factor, however, it is within the invention to delete ROM
39 and provide another ROM to replace RAM 51 (see FIG. 6A). The ROM
substituted for RAM 51 will contain B(f) and supply this to the
multiplier function 54 whenever required.
* * * * *